Using improved operator product expansion in Borel-Laplace sum rules with ALEPH τ decay data, and determination of pQCD coupling

We use improved truncated operator product expansion (OPE) for the Adler function, involving two types of terms with dimension D = 6, in the double-pinched Borel-Laplace sum rules and finite energy sum rules for the V + A channel strangeless semihadronic tau decays. The generation of the higher order perturbative QCD terms of the D = 0 part of the Adler function is carried out using a renormalon-motivated ansatz incorporating the leading UV renormalon and the first two leading IR renormalons. The trunacted D = 0 part of the sum rules is evaluated by two variants of the fixed-order perturbation theory (FO), by principal value of the Borel resummation (PV), and by contourimproved perturbation theory (CI). For the experimental V + A channel spectral function we use the ALEPH tau-decay data. We point out that the truncated FO and PV evaluation methods account correctly for the renormalon structure of the sum rules, while this is not the case for the truncated CI evaluation. We extract the value of the (MS) over bar coupling alpha(s)(m(tau)(2)) = 0.3235(-0.0128)(+0.0138) [alpha(s)(M-Z(2)) = 0.1191 +/- 0.0016] for the average of the two FO methods and the PV method, which we consider as our main result. If we included in the average also CI extraction, the value would be alpha(s)(m(tau)(2))= 0.3299(-0.0028)(+0.0026)]. This work is an extension and improvement of our previous work (Ayala et al. in Eur Phys J. C 81(10): 930, 2021, arXiv:2105.00356 [hep-ph]) where we used for the truncated OPE a more naive (and widely used) form and where the extracted values for alpha(s)(M-Z(2)) were somewhat lower.

Automated summary

This paper uses an improved truncated operator product expansion method to calculate the Adler function in V + A channel strangeless semihadronic tau decays. The values of the coupling constant αs(m(τ)²) are obtained through different evaluation methods.